High Dive – Trig Unit



UNIT 6 – Trigonometric Functions

High Dive – The Circus Act Problem Activity #4

Extending the Sine Reference/ Testing the Definition

If the Ferris wheel turns counterclockwise at a constant angular speed of 9 degrees per second, and the platform passes the 3 o’clock position at t = 0, then the platform will remain in the first quadrant through t = 10.

During this time interval, the platform’s height above the ground is given by the formula

[pic]

But the right-triangle definition of the sine function makes sense only for acute angles. You’ve seen that the sine function can be extended to all angles using the xy-coordinate system. The big question is this:

If you use this coordinate definition of the sine function, does the platform height formula work for all angles?

Your task in this activity is to investigate that question.

1) If the platform has been turning for 25 seconds, then it has moved through an angle of [pic] and is now in the third quadrant of its cycle.

a) Use a diagram like the one shown here to find the value of [pic] based on the coordinate definition of the sine function (Suggestion: Choose a specific value of y using the right triangle in the third quadrant.)

b) Substitute your answer from Question 1a into the expression [pic].

c) Explain why your answer in Question 1b is a reasonable answer for the position of the platform after 25 seconds.

d) Verify that your calculator gives the same value for [pic]that you found in Question 1a.

2) Go through a sequence of steps like those in Question 1, but use the value t = 32, which places the platform in the third quadrant. (You will first need to find the actual height of the platform for t = 32.)

Graphing the Ferris Wheel

1) Plot individual points to create a graph showing the platform’s height, h, as a function of the time elapsed, t. Explain how you get the value for h for each point you plot. Your graph should show the first 80 seconds of the Ferris wheel’s movement.

Reminder: Use the same basic information about the Ferris Wheel given previously.

2) Describe in words how this graph would change if you made each of the changes described in Questions 2a through 2c. Treat each question as a separate problem, changing only the item mentioned in that problem and keeping the rest of the information as in Question 1.

a) How would the graph change if the radius of the Ferris wheel was smaller?

b) How would the graph change if the Ferris wheel was turning faster (that is, if the period was shorter?)

c) How would the graph change if you measured height with respect to the center of the Ferris wheel instead of with respect to the ground? (For example, if the platform was 40 feet above the ground, you would treat this as a height of -25, because 40 feet above the ground is 25 feet below the center of the Ferris wheel.)

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download